Generation of a hologram pattern

ABSTRACT

Device for generating a hologram pattern including selecting means for selecting, as cross section ranges which are in a plurality of cross sections parallel to hologram pattern in 3D object and which are ranges used for generating hologram pattern, cross section ranges which overlap ranges in other cross sections when the relevant cross section is perspectively seen from a predetermined observation point on the hologram pattern; depth integrating means for calculating, for lattice points in one cross section range, a depth integral function acquired by integrating an inverse diffraction function for determining hologram pattern for displaying points of 3D object with respect to respective lattice points in the cross section ranges which overlap the relevant lattice point; and inverse Fourier transform means for generating hologram pattern by performing two-dimensional inverse transform on depth integral functions with respect to plurality of lattice points in one cross section range.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a divisional application from U.S. patent application Ser. No.10/910,670 filed Aug. 3, 2004.

FIELD OF THE INVENTION

The present invention relates to a generation device, a generationmethod, a program, and a recording medium for generating a hologrampattern. It also relates to generating a hologram pattern using acomputer, wherein the hologram pattern displays a 3D object based on the3D object to be displayed.

BACKGROUND OF THE INVENTION

Heretofore, holography technology capable of causing an observer toperceive a three-dimensional object has been used. Since holographytechnology does not require a special device and the like and can causean observer to intuitively and correctly perceive a 3D object withoutimposing a strain on the eye of the observer, holography technology hasa wide range of applications. For example, holography technology is usedin the fields of exhibition, advertisement, medical care, education,entertainment, and the like.

The principle of holography technology will be described. FIG. 6 showsan example of a hologram optical generation system 60 for opticallygenerating a hologram pattern. The hologram optical generation system 60includes a lighting fixture 610, a light-emitting device 620, a hologram630, and a light-emitting device 640. First, the hologram opticalgeneration system 60 performs the processing below in order to generatethe interference of light (S62). The lighting fixture 610 irradiateslight to an object 600 to be displayed. The object 600 reflects thelight irradiated from the lighting fixture 610 as an object beam ontothe hologram 630. The light-emitting device 620 irradiates a referencebeam to the hologram 630. Thus, interfering light in which the objectand reference beams interfere with each other is generated.

The hologram 630 records the wavelength and phase of the interferinglight generated in S62 as an interference pattern (S64). For example,the hologram 630 is a predetermined optical film and is exposed to theinterfering light to record the wavelength and phase of the interferinglight. The light-emitting device 640 irradiates the reference beam tothe hologram 630 (S66). The hologram 630 diffracts the reference beamirradiated from the light-emitting device 640 with the interferencepattern and reflects the reference beam as a reconstructed beam towardan observer. The observer perceives the wavelength and phase of lightrecorded on the hologram 630 by observing the reconstructed beam (S68).Thus, the observer can perceive a 3D object 650, which is the same asthe object 600.

In what follows, consideration is given to the following documents:

-   Non-patent Literature 1) High-Speed Holographic-Stereogram    Calculation Method Using 2D FFT, SPIE, Vol. 3010, p 49-   Non-patent Literature 2) Recurrence formulas for fast creation of    synthetic three-dimensional hologram, Applied Optics, Vol. 39, No.    35, p 6587

Moreover, in recent years, with the progress of computers and the trendtoward higher definitions of LCD panels, a method of generating ahologram pattern using a computer to display the hologram pattern usingan LCD panel is receiving attention (e.g., refer to Non-patentLiterature 1 and Non-patent Literature 2). Known methods are dividedinto, for example, the following two groups:

Method 1

An object is regarded as a set of point light sources. Then, for eachpoint light source, Fresnel-Kirchhoff integral, which determines a lightwave coming from the point light source, is calculated.

Method 2

For each of cross sections when an object is divided into planesperpendicular to the depth direction, a diffraction pattern, e.g., aFraunhofer diffraction pattern, a Fresnel diffraction pattern, or aFourier diffraction pattern, generated by light coming from the relevantcross section, is integrated in the depth direction.

In general, optically manufacturing a hologram pattern requires variousequipment, e.g., a device for generating a predetermined reference beam,a film for recording an interference pattern, a darkroom for exposing ahologram, and the like. In particular, optically manufacturing ahologram for reconstructing a moving image requires enormous cost andtime.

Moreover, a known method of electronically generating a hologram alsorequires enormous computation time. For example, in a knowntwo-dimensional image, each pixel is related to each portion of anobject to be displayed. On the other hand, each pixel of a hologrampattern needs to record interfering light of a light wave coming fromthe entire object to be displayed. Accordingly, the creation of ahologram pattern requires more calculations compared with the case wheregeneral three-dimensional computer graphics are generated.

For example, according to the above-described Method 1, the computationtime required for the creation of a hologram is proportional to theproduct of the number of pixels of the hologram, the number of pointlight sources, and the computation time in which one point light sourcedetermines one pixel. In the case where a moving image is created bythis method using a computer, computing performance as high as severalpetaflops is required. On the other hand, according to Method 2,computation time is proportional to the product of the computation timefor determining a hologram pattern from one cross section and the numberof cross sections. This method also requires computing performance ofapproximately 100 gigaflops to 1 teraflops.

SUMMARY OF THE INVENTION

In order to solve the above problems, a first aspect of the presentinvention provides a generation device for generating a hologram patternfor displaying a 3D object based on the 3D object to be displayed, thegeneration device including: selecting means for selecting, as a crosssection range in each cross section of a plurality of cross sectionsinto which the 3D object is divided and which are parallel to thehologram pattern, the cross section range to be used for generating thehologram pattern, a cross section range overlapping cross section rangesin other cross sections in a case where the relevant cross section isperspectively seen from a previously determined observation point on thehologram pattern; depth integrating means for calculating, for each of aplurality of lattice points in a coordinate system provided in one crosssection range, a depth integral function acquired by integrating aninverse diffraction function for determining a hologram pattern fordisplaying points of the 3D object, with respect to respective latticepoints in the plurality of cross section ranges, the respective latticepoints overlapping the relevant lattice point in a case where theplurality of cross section ranges are perspectively seen from theobservation point; and inverse Fourier transform means for generatingthe hologram pattern by performing a two-dimensional inverse Fouriertransform on the depth integral functions with respect to the pluralityof lattice points in the one cross section range, a generation methodusing the generation device, a program for causing a computer tofunction as the generation device, and a recording medium having theprogram recorded thereon.

Note that the above-described summary of the invention does not list allfeatures necessary for the present invention and that subcombinations ofthese features can be also included in the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and theadvantages thereof, reference is now made to the following descriptiontaken in conjunction with the accompanying drawings.

FIG. 1 is a diagram for explaining functional blocks and the concepts offunctions of a generation device 10.

FIG. 2 shows an operation flow of the generation device 10.

FIG. 3 shows a block diagram of a generation device 10 in a modifiedexample.

FIG. 4 shows an operation flow of the generation device 10 in themodified example.

FIG. 5 shows one example of the hardware configuration of the generationdevice 10 in the embodiment or the modified example.

FIG. 6 shows an example in which a hologram pattern is opticallygenerated.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides generation devices, methods and apparatusfor generating a hologram pattern for displaying a 3D object based onthe 3D object to be displayed. An example of a generation deviceincludes: selecting means for selecting, as a cross section range ineach cross section of a plurality of cross sections into which the 3Dobject is divided and which are parallel to the hologram pattern, thecross section range to be used for generating the hologram pattern, across section range overlapping cross section ranges in other crosssections in a case where the relevant cross section is perspectivelyseen from a previously determined observation point on the hologrampattern; depth integrating means for calculating, for each of aplurality of lattice points in a coordinate system provided in one crosssection range, a depth integral function acquired by integrating aninverse diffraction function for determining a hologram pattern fordisplaying points of the 3D object, with respect to respective latticepoints in the plurality of cross section ranges, the respective latticepoints overlapping the relevant lattice point in a case where theplurality of cross section ranges are perspectively seen from theobservation point; and inverse Fourier transform means for generatingthe hologram pattern by performing a two-dimensional inverse Fouriertransform on the depth integral functions with respect to the pluralityof lattice points in the one cross section range, a generation methodusing the generation device, a program for causing a computer tofunction as the generation device, and a recording medium having theprogram recorded thereon.

Hereinafter, the present invention will be described by way ofadvantageous embodiments. However, the embodiments below are notintended to limit the invention commensurate with the scope of theclaims, and all combinations of the features described in the embodimentare not necessarily indispensable for solving means of the invention.

FIG. 1 is a diagram for explaining functional blocks and the concepts offunctions of a generation device 10. The generation device 10 is adevice which, based on a 3D object to be displayed as a diffractionpattern, generates and displays a hologram pattern for displaying the 3Dobject. Using the present drawing, a method in which the generationdevice 10 displays a hologram pattern on an LCD 145 in order to cause anobserver to perceive a 3D object 105 will be described.

The generation device 10 includes a 3D object database 100, selectingmeans 110, depth integrating means 120, inverse Fourier transform means130, display means 140, and the LCD 145 for displaying the hologrampattern. The 3D object database 100 acquires data representing the 3Dobject to be displayed from other device or the like communicatingtherewith through a network and stores the data. Instead of this, the 3Dobject database 100 may acquire data representing the 3D object to bedisplayed from a three-dimensional scanner for reading the shape of anobject to be displayed and store the data. For example, the 3D object tobe displayed is a 3D object which the observer perceives as the resultof seeing the hologram pattern on the LCD 145.

The selecting means 110 acquires the data representing the 3D object tobe displayed, e.g., data representing the shape or the like of the 3Dobject 105, from the 3D object database 100. Then, the selecting means110 selects cross section ranges 115-1 to 115-N, which are ranges usedfor generating the hologram pattern, in a plurality of respective crosssections into which the 3D object 105 is divided and which are parallelto the LCD 145, and transmits information for identifying the crosssection ranges 115-1 to 115-N to the depth integrating means 120.

Specifically, the selecting means 110 selects, as each of the crosssection ranges 115-1 to 115-N in the respective cross sections, a rangeoverlapping the cross section ranges in the other cross sections in thecase where the relevant cross section is perspectively seen from apreviously determined observation point 148 on the hologram pattern.

For each of a plurality of lattice points in a coordinate systemprovided in one cross section range, the depth integrating means 120calculates a depth integral function acquired by integrating an inversediffraction function for determining a hologram pattern for displayingpoints of the 3D object, with respect to the respective lattice pointsin the plurality of cross section ranges which overlap the relevantlattice point when the plurality of cross section ranges areperspectively seen from the observation point 148, and transmits thecalculation result to the inverse Fourier transform means 130.

For example, for u(X₁, Y₁, z₁), which is a lattice point in the crosssection range 115-1, the depth integrating means 120 calculates, as adepth integral function, a function acquired by integrating the inversediffraction function with respect to u(X₃, Y₃, z₂), u(X₅, Y₅, z₃), andthe like, which are the lattice points in the respective cross sectionranges 115-1 to 115-N that overlap u(X₁, Y₁, z₁) in the case where thecross section ranges 115-1 to 115-N are perspectively seen from theobservation point 148.

Moreover, for u(X₂, Y₂, z₁), which is a lattice point in the crosssection range 115-1, the depth integrating means 120 calculates, as adepth integral function, a function acquired by integrating the inversediffraction function with respect to u(X₄, Y₄, z₂), u(X₆, Y₆, z₃), andthe like, which are the lattice points in the respective cross sectionranges 115-1 to 115-N that overlap u(X₂, Y₂, z₁) in the case where thecross section ranges 115-1 to 115-N are perspectively seen from theobservation point 148.

The inverse Fourier transform means 130 generates a hologram pattern byperforming a two-dimensional inverse discrete Fourier transform, whichis one example of a two-dimensional inverse Fourier transform, on thedepth integral functions received from the depth integrating means 120,with respect to the plurality of lattice points in the one cross sectionrange, e.g., with respect to u(X₁, Y₁, z₁), u(X₂, Y₂, z₁), and the like,and transmits the hologram pattern to the display means 140. In thisway, the inverse Fourier transform means 130 performs an inverse Fouriertransform once in order to generate one hologram pattern. This enablesthe generation device 10 to generate the hologram pattern fast.

Here, lattice points are, for example, points to be discretized in atwo-dimensional inverse discrete Fourier transform performed by theinverse Fourier transform means 130.

The display means 140 displays the hologram pattern received from theinverse Fourier transform means 130 on the LCD 145. Thus, the LCD 145can cause the observer to perceive the 3D object 105 as holography.

FIG. 2 shows an operation flow of the generation device 10. Theselecting means 110 selects the cross section ranges 115-1 to 115-N,which are ranges used for generating the hologram pattern, in theplurality of respective cross sections into which the 3D object 105 isdivided and which are parallel to the LCD 145 (S200). This will beconcretely described using the following procedure.

1. Periodicity of Hologram Pattern

The diffraction pattern u(X, Y, z) reconstructed on the cross section ata distance z from the hologram pattern in the case where h(x, y)representing the hologram pattern on a hologram H is perpendicularlyirradiated with coherent light at a wavelength λ, is determined by theFraunhofer diffraction integral function given by Eq. 1 below.

$\begin{matrix}{{u\left( {X,Y,z} \right)} = {{^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{\int{\int_{H}\ {{x}{y}\; {h\left( {x,y} \right)}^{{- 2}\; {{\pi }{({{\xi \; x} + {\zeta \; y}})}}}}}}}_{{\xi = \frac{X}{\lambda \; z}},{\zeta = \frac{Y}{\lambda \; z}}}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where k=2π/λ and k represents the wave number of the light wave.

Using a Fourier transform, the integral on the right-hand side can beexpressed as follows:

$\begin{matrix}{{u\left( {X,Y,z} \right)} = {^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{F\lbrack h\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

Moreover, since the display means 140 displays the hologram patternusing pixels arranged on the LCD 145, the hologram pattern h(x, y) canbe expressed as Eq. 3 below.

$\begin{matrix}{{h\left( {x,y} \right)} = {\sum\limits_{n,m}{g_{n,m}{\chi \left( {{x - {n\; \Delta}},{y - {m\; \Delta}}} \right)}}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

where g_(n,m) represents the color displayed in the pixel at coordinates(n, m) on the LCD 145. Moreover, χ(x, y) represents the aperturefunction of each pixel. Furthermore, Δ represents the inter-pixeldistance of the LCD 145 for displaying the hologram pattern.

Under the above conditions, u(X, Y, z) representing the diffractionpattern is determined by Eq. 4 below.

$\begin{matrix}\begin{matrix}{{u\left( {X,Y,z} \right)} = {^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{F\lbrack h\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)}} \\{= ^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}} \\{{{F\left\lbrack {\sum\limits_{n,m}{g_{n,m}{\chi \left( {{x - {n\; \Delta}},{y - {m\; \Delta}}} \right)}}} \right\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)}} \\{= ^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}} \\{{\sum\limits_{n,m}{g_{n,m}{F\left\lbrack {\chi \left( {{x - {n\; \Delta}},{y - {m\; \Delta}}} \right)} \right\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)}}} \\{= {^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{\sum\limits_{n,m}{g_{n,m}^{{- 2}\; {{\pi }({{n\frac{X\; \Delta}{\lambda \; z}} + {m\frac{Y\; \Delta}{\lambda \; z}}})}}}}}} \\{{{F\lbrack\chi\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)}}\end{matrix} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

Here, Eq. 6 below is the Fourier transform of the aperture function andtherefore represents the contrast of the entire plane on which thediffraction pattern is displayed. That is, Eq. 7 below is a termrepresenting the shape of the diffraction pattern.

$\begin{matrix}^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}} & \left( {{Equation}\mspace{14mu} 5} \right) \\{{F\lbrack\chi\rbrack}\left( {\frac{X}{\lambda \; z},\frac{Y}{\lambda \; z}} \right)} & \left( {{Equation}\mspace{14mu} 6} \right) \\{{G\left( {X,Y} \right)} \equiv {\sum\limits_{n,m}{g_{n,m}^{{- 2}\; {{\pi }{({{n\frac{X\; \Delta}{\lambda \; z}} + {m\frac{Y\; \Delta}{\lambda \; z}}})}}}}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

Here, Eq. 7 is a Fourier series having g_(n,m) as coefficients andtherefore has periodicity of λz/Δ for each of X and Y. That is, Eq. 4 asa whole, except for Eq. 5 representing the phase of the light wave andEq. 6 representing the contrast of the entire plane, has periodicity ofλz/Δ.

2. Determination of Hologram Pattern Using Inverse Function ofFraunhofer Diffraction Integral Function

The hologram pattern h(x, y) for displaying the diffraction pattern u(X,Y, z) is determined by Eq. 8 below, which is the inverse function of theFraunhofer diffraction integral function.

$\begin{matrix}{{h\left( {x,y} \right)} = {{\int{\int_{H}\ {{X}{Y}\; ^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{u\left( {X,Y,z} \right)}^{{- 2}\; {{\pi }{({{\alpha \; X} + {\beta \; Y}})}}}}}}_{{\alpha = \frac{x}{\lambda \; z}},{\beta = \frac{y}{\lambda \; z}}}}} & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

Here, the inverse diffraction function according to the presentinvention is, for example, an integrand with respect to coordinatevariables in Eq. 8, which is the inverse function of the Fraunhoferdiffraction integral function.

Using an inverse Fourier transform, the integral on the right-hand sidecan be expressed as follows:

$\begin{matrix}{{h\left( {x,y} \right)} = {{F^{- 1}\left\lbrack {^{\; {k({z + \frac{X^{2} + Y^{2}}{2\; z}})}}{u\left( {X,Y,z} \right)}} \right\rbrack}\left( {\frac{x}{\lambda \; z},\frac{y}{\lambda \; z}} \right)}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

3. Selection of Cross Section Ranges 115-1 to 115-N by Selecting Means110

The selecting means 110 selects the cross section ranges 115-1 to 115-Nby setting the integration interval in the inverse function of theFraunhofer diffraction integral function to the period described in theforegoing “1. Periodicity of Hologram Pattern.”

First, as expressed by Eqs. 10 and 11, in the inverse diffractionfunction of Eq. 8, the selecting means 110 performs a variable changefrom X and Y, which are coordinate variables representing coordinates ineach of the plurality of cross sections, to the variables acquired bydividing X and Y by the distance to the relevant cross section.

$\begin{matrix}{\overset{\_}{X} = \frac{\Delta \; X}{\lambda \; z}} & \left( {{Equation}\mspace{14mu} 10} \right) \\{\overset{\_}{Y} = \frac{\Delta \; Y}{\lambda \; z}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

Moreover, in Eq. 8, the selecting means 110 sets the integrationinterval with respect to the coordinate variables after the variablechange, to the same previously determined interval, e.g., the intervalof 0 to 1, for each of the cross section ranges 115-1 to 115-N.Therefore, Eq. 8 is modified into Eq. 12 below.

$\begin{matrix}\begin{matrix}{{h\left( {x,y} \right)} = {\int{\int_{{\lbrack{0,1}\rbrack} \times {\lbrack{0,1}\rbrack}}\ {{\overset{\_}{X}}{\overset{\_}{Y}}^{\; {{kz}({1 + {\frac{\Delta^{2}}{2}{({{\overset{\_}{X}}^{2} + {\overset{\_}{Y}}^{2}})}}})}}}}}} \\{{{{u\left( {{\frac{\lambda \; z}{\Delta}\overset{\_}{X}},{\frac{\lambda \; z}{\Delta}\overset{\_}{Y}},z} \right)}^{{- 2}\; {{\pi }{({{\alpha \frac{\lambda \; z}{\Delta}X} + \frac{\lambda \; z}{\Delta}})}}}}_{{\alpha = \frac{x}{\lambda \; z}},{\beta = \frac{y}{\lambda \; z}}}}} \\{= {\int{\int_{{\lbrack{0,1}\rbrack} \times {\lbrack{0,1}\rbrack}}\ {{\overset{\_}{X}}{\overset{\_}{Y}}^{\; {{kz}({1 + {\frac{\Delta^{2}}{2}{({{\overset{\_}{X}}^{2} + {\overset{\_}{Y}}^{2}})}}})}}}}}} \\{{{{u\left( {{\frac{\lambda \; z}{\Delta}\overset{\_}{X}},{\frac{\lambda \; z}{\Delta}\overset{\_}{Y}},z} \right)}^{{- 2}\; {{\pi }{({{\alpha \; X} + {\beta \; Y}})}}}}_{{\alpha = \frac{x}{\Delta}},{\beta = \frac{y}{\Delta}}}}}\end{matrix} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

Note that a constant term concerning the entire equation is omittedhere.

Therefore, the integration interval with respect to each of X and Ybecomes the interval of 0 to λz/Δ. That is, the selecting means 110selects, as each of the cross section ranges 115-1 to 115-N, a rangehaving sides in the X and Y directions which are proportional to thedistance from the LCD 145 to the relevant cross section and thewavelength of the light wave and inversely proportional to theinter-pixel distance of the LCD 145. Thus, the selecting means 110 canselect the plurality of cross section ranges in the plurality ofrespective cross sections into which the 3D object 105 is divided andwhich are parallel to the LCD 145 such that the plurality of crosssection ranges overlap when perspectively seen from the observationpoint 148 on the LCD 145.

Subsequently, for each of a plurality of lattice points in one crosssection range, the depth integrating means 120 calculates a depthintegral function acquired by integrating the inverse diffractionfunction for determining the hologram pattern for displaying points ofthe 3D object, with respect to the respective lattice points in theplurality of cross section ranges which overlap the relevant latticepoint in the case where the plurality of cross section ranges areperspectively seen from the observation point 148 (S210).

A concrete example will be described. First, the present example isbased on the premise that the LCD 145 has pixels arranged in N rows andN columns. Moreover, the depth integrating means 120 determines latticepoints which overlap each other in the respective cross section ranges115-1 to 115-N in the case where the cross section ranges 115-1 to 115-Nare perspectively seen from the observation point 148, such that thelattice points are related to each of the pixels in the LCD 145. Thus,the inverse diffraction function representing the lattice points of the3D object is given by Eq. 14. Note that the first and second terms ofthe integrand of Eq. 12, excluding the last exponential function, areomitted and expressed as Eq. 13.

$\begin{matrix}{{{\overset{\_}{u}}^{E}\left( {\overset{\_}{X},\overset{\_}{Y},z} \right)} \equiv {^{\; {{kz}({1 + {\frac{\Delta^{2}}{2}{({{\overset{\_}{X}}^{2} + {\overset{\_}{Y}}^{2}})}}})}}{u\left( {{\frac{\lambda \; z}{\Delta}\overset{\_}{X}},{\frac{\lambda \; z}{\Delta}\overset{\_}{Y}},z} \right)}}} & \left( {{Equation}\mspace{14mu} 13} \right) \\{{{{\overset{\_}{u}}_{I,J}^{E}(z)} \equiv {{\overset{\_}{u}}^{E}\left( {\frac{I}{N},\frac{J}{N},z} \right)}}\mspace{14mu} \left( {I,{J = 0},{1\mspace{11mu} \ldots}\mspace{14mu},{N - 1}} \right)} & \left( {{Equation}\mspace{14mu} 14} \right)\end{matrix}$

Therefore, the depth integrating means 120 can determine the hologrampattern for displaying lattice points on one cross section of the 3Dobject, as the function represented by Eq. 15 below.

$\begin{matrix}{{{{h_{i,j}(z)} \equiv {h\left( {\frac{\Delta \; i}{N},\frac{\Delta \; j}{N}} \right)}} = {{DF}^{- 1}\left\lbrack {{\overset{\_}{u}}_{I,J}^{E}(z)} \right\rbrack}}\left( {i,{j = {01\ldots}}\mspace{14mu},{N - 1}} \right)} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$

Here, the hologram pattern for displaying the 3D object can be generatedby integrating Eq. 15 with respect to z. For example, Eq. 16 iscalculated.

h _(i,j) ≡∫dzDF ⁻¹ [ū ^(E) _(I,J)(z)](i,j=0, 1 . . . , N−1)  (Equation16)

However, in order to calculate Eq. 16 as it is, a two-dimensionalinverse discrete Fourier transform needs to be performed a number oftimes corresponding to the number of cross sections. On the other hand,if the processing sequence of the two-dimensional inverse discreteFourier transform and the integral with respect to z can be reversed,the number of times of processing the two-dimensional inverse discreteFourier transform can be reduced to one. Accordingly, the computationtime can be reduced.

Hereinafter, the reason why the processing sequence can be reversed willbe described.

Eq. 12 determining the diffraction pattern represents the processing ofperforming a two-dimensional inverse Fourier transform on the expressionu(X, Y, z) which determines the diffraction pattern and then integratingthe result with respect to the variable z in the depth direction.Moreover, the two-dimensional inverse Fourier transform is an integraltransform with respect to the coordinate variables after the variablechange, and the integration interval thereof is 0 to 1. That is, sinceEq. 12 is the integral of a cuboid region in the three-dimensionalcoordinate system after the variable change, the processing sequence ofthe two-dimensional inverse Fourier transform and the integratingprocessing can be reversed.

Here, in Eq. 16, a processing corresponding to the two-dimensionalinverse Fourier transform in Eq. 12 is discretized and performed as atwo-dimensional inverse discrete Fourier transform. Therefore, in Eq.16, the processing sequence of the calculation of the seriescorresponding to the two-dimensional inverse discrete Fourier transformand the processing of integrating with respect to the variable z in thedepth direction can be reversed. As a result, the depth integratingmeans 120 can perform the integral with respect to z before thetwo-dimensional inverse discrete Fourier transform for the expressionu(X, Y, z) determining the diffraction pattern.

Furthermore, the depth integrating means 120 approximates the term (17)representing the phase of the light wave in the inverse diffractionfunction represented in Eq. 12 by a function independent of thecoordinate variables, e.g., Eq. 18. Therefore, the depth integratingmeans 120 can perform the integral with respect to z before thetwo-dimensional inverse discrete Fourier transform also for the termrepresenting the phase of the light wave.

$\begin{matrix}^{\; {{kz}({1 + {\frac{\Delta^{2}}{2}{({{\overset{\_}{X}}^{2} + {\overset{\_}{Y}}^{2}})}}})}} & \left( {{Equation}\mspace{14mu} 17} \right) \\^{\; {kz}} & \left( {{Equation}\mspace{14mu} 18} \right)\end{matrix}$

Instead of the above, the depth integrating means 120 may approximatethe term (17) representing the phase of the light wave by a periodicfunction having, as the period of the coordinate variables, the ratio ofthe coordinate variables before the variable change to the coordinatevariables after the variable change, e.g., a periodic function having apredetermined value with period λz/Δ. This approximation also enablesthe depth integrating means 120 to integrate the inverse diffractionfunction with respect to z prior to the two-dimensional inverse discreteFourier transform.

As described above, the depth integrating means 120 can calculate thedepth integral function by integrating the inverse diffraction functionin which the variable change has been performed, with respect to thevariable z representing the distance from the hologram pattern to across section.

Subsequently, the inverse Fourier transform means 130 performs atwo-dimensional inverse discrete Fourier transform on the depth integralfunctions with respect to a plurality of lattice points in one crosssection range for the coordinate variables after the variable change(S220). Thus, the inverse Fourier transform means 130 can generate thehologram pattern. The procedures of S210 and S220 are represented by Eq.19.

h _(i,j) ≡DF ⁻¹ [∫dzū ^(E) _(I,J)(z)](i,j=0, 1 . . . , N−1)  (Equation19)

Then, the display means 140 displays the hologram pattern generated bythe inverse Fourier transform means 130 on the LCD 145 (S230).

As described above in the present embodiment, the generation device 10executes the integrating processing with respect to a variablerepresenting the distance from the diffraction pattern to be displayedto the hologram pattern before the two-dimensional inverse discreteFourier transform by appropriately determining the integration intervalof the inverse diffraction function and the granularity ofdiscretization. Thus, the number of times of a two-dimensional inversediscrete Fourier transform can be drastically reduced.

FIG. 3 shows a block diagram of a generation device 10 in a modifiedexample. The generation device 10 in the present example has atwo-dimensional image database 150, distance information acquiring means160, and inverse diffraction function generating means 170 in additionto the components of the generation device 10 of FIG. 1. Moreover, thegeneration device 10 in the present example does not have to include the3D object database 100, the selecting means 110, and the depthintegrating means 120.

The two-dimensional image database 150 stores information representingeach pixel of a two-dimensional image acquired by projecting the 3Dobject to be displayed as a diffraction pattern onto a predeterminedplane such that the information is associated with distance informationrepresenting the distance from the relevant pixel to a portion of the 3Dobject recorded as the relevant pixel. Moreover, the two-dimensionalimage database 150 may acquire the two-dimensional image from otherdevice communicating therewith through a network.

For example, the two-dimensional image database 150 may store atwo-dimensional image in conformity with the OpenGL standard, which isan API for processing graphics. In this case, the two-dimensional imagedatabase 150 stores data in the z-buffer conforming to the OpenGLstandard as the distance information. To be more precise, for the pixelhaving (X-coordinate, Y-coordinate)=(1, 0) of the two-dimensional image,the two-dimensional image database 150 stores 0x0010 representing colorsor the like of the relevant pixel as information representing therelevant pixel and 0xC3 as the distance information of the relevantpixel. Note that the two-dimensional image database 150 may store atwo-dimensional image having a data size compressed by a predeterminedprocessing.

Then, the distance information acquiring means 160 acquires theinformation representing each pixel of the relevant two-dimensionalimage from the two-dimensional image database 150 such that theinformation is associated with the distance information of the relevantpixel, and transmits the acquired information to the inverse diffractionfunction generating means 170. For each pixel of the two-dimensionalimage, the inverse diffraction function generating means 170 generatesan inverse diffraction function for determining a hologram pattern fordisplaying a portion of the 3D object recorded as the relevant pixel,based on the distance information at the relevant pixel, transmits theinverse diffraction function to the inverse Fourier transform means 130.

The inverse Fourier transform means 130 generates a hologram pattern byperforming a two-dimensional inverse discrete Fourier transform on thereceived inverse diffraction functions with respect to variablesrepresenting the coordinates of the two-dimensional image, and transmitsthe hologram pattern to the display means 140. The display means 140displays the received hologram pattern on the LCD 145.

FIG. 4 shows an operation flow of the generation device 10 in themodified example. The distance information acquiring means 160 acquiresdistance information for each pixel of a two-dimensional image acquiredby projecting a 3D object to be displayed as a diffraction pattern ontoa predetermined plane (S400). Then, for each pixel of thetwo-dimensional image, the inverse diffraction function generating means170 generates an inverse diffraction function for determining thehologram pattern for displaying a portion of the 3D object recorded asthe relevant pixel, based on the distance information at the relevantpixel (S410).

For example, the inverse diffraction function is an integrand in theinverse function of the Fraunhofer diffraction integral function. Inthis case, the inverse diffraction function generating means 170generates the term representing the phase of the light wave in therelevant inverse diffraction function based on the distance information.

The inverse Fourier transform means 130 generates the hologram patternby performing a two-dimensional inverse discrete Fourier transform onthe inverse diffraction functions with respect to variables representingcoordinates of the two-dimensional image (S420). The display means 140displays the hologram pattern on the LCD 145 (S430).

As described above, according to the present modified example, thegeneration device 10 can generate a hologram pattern based on anexisting two-dimensional image in conformity with the OpenGL standard orthe like. Thus, a user can easily make the existing two-dimensionalimage three-dimensional. Moreover, similar to the generation device 10in the embodiment, the generation device 10 can generate a hologrampattern very fast by performing two-dimensional inverse discrete Fouriertransform once.

FIG. 5 shows one example of the hardware configuration of the generatingdevice 10 in the embodiment or the modified example. The generationdevice 10 includes a CPU peripheral section having a CPU 1000, a RAM1020, a graphic controller 1075, and an LCD 145 which are connected toeach other through a host controller 1082; an input/output sectionhaving a communication interface 1030, a hard disk drive 1040, and aCD-ROM drive which are connected to the host controller 1082 through aninput/output controller 1084; and a legacy input/output section having aROM 1010, a floppy disk drive 1050, and an input/output chip 1070 whichare connected to the input/output controller 1084.

The host controller 1082 connects the RAM 1020 with the CPU 1000 and thegraphic controller 1075 which access the RAM 1020 at high transferrates. The CPU 1000 performs an operation based on programs stored inthe ROM 1010 and the RAM 1020 and controls each unit. The graphiccontroller 1075 acquires image data which the CPU 1000 or the likegenerates on a frame buffer provided in the RAM 1020, and displays theimage data on the LCD 145. Instead of this, the graphic controller 1075may include a frame buffer inside, which stores image data generated bythe CPU 1000 or the like.

The input/output controller 1084 connects the host controller 1082 withthe communication interface 1030, the hard disk drive 1040, and theCD-ROM drive 1060, which are relatively fast input/output devices. Thecommunication interface 1030 communicates with an external devicethrough a network. The hard disk drive 1040 stores programs and dataused by the generation device 10. The CD-ROM drive 1060 reads a programor data from the CD-ROM 1095, and provides the program or the data forthe input/output chip 1070 through the RAM 1020.

Moreover, the ROM 1010 and the floppy disk drive 1050, the input/outputchip 1070, and the like, which are relatively slow input/output devices,are connected to the input/output controller 1084. The ROM 1010 stores aboot program executed by the CPU 1000 when the generation device 10 isstarted, and a program dependent on the hardware of the generationdevice 10 and the like. The floppy disk drive 1050 reads a program ordata from the floppy disk 1090, and provides the program or the data forthe input/output chip 1070 through the RAM 1020. The input/output chip1070 is connected to the floppy disk 1090 and various kinds ofinput/output devices through, for example, a parallel port, a serialport, a keyboard port, a mouse port, and the like.

A program provided to the generation device 10 is provided by a user, ina state of being stored on a recording medium, such as the floppy disk1090, the CD-ROM 1095, an IC card, or the like. The program is read fromthe recording medium through the input/output chip 1070 and/or theinput/output controller 1084, and installed on the generation device 10to be executed.

The program installed and executed on the generation device 10 includesa selecting module, a depth integrating module, an inverse Fouriertransform module, and a display module. The operation which each moduleactuates the generation device 10 to perform is the same as that of thecorresponding member in the generation device 10 described in FIGS. 1 to4. Therefore, a description thereof will be omitted.

The above-described programs and modules may be stored on an externalrecording medium. In addition to the floppy disk 1090 and the CD-ROM1095, optical recording media including DVDs and PDs, magneto-opticalrecording media including MDs, tape media, semiconductor memoriesincluding IC cards, and the like can be used as the recording medium.Moreover, a program may be provided to the generation device 10 througha network using, as the recording medium, a storage device such as ahard disk drive or a RAM, which is provided on a server system connectedto a dedicated communication network or the Internet.

As apparent from the above description, the generation device 10 cangenerate a hologram pattern for displaying a desired 3D object fast.Specifically, the generation device 10 widely sets the integrationinterval of an inverse diffraction function for determining a hologrampattern for displaying one point of the 3D object, depending on thedistance between the hologram pattern and a cross section of the 3Dobject. Thus, the generation device 10 reverses the processing sequenceof an integrating processing and an inverse Fourier transform to reducethe number of times of an inverse Fourier transform.

Moreover, the generation device 10 has a high affinity for knownstandards. Specifically, the generation device 10 can generate ahologram pattern for displaying a two-dimensional image in conformitywith the OpenGL standard as a 3D object.

Thus, the generation device 10 can generate a hologram pattern very fastcompared with a known device. This makes it possible to realize movingimage reconstruction by holography using a computer having realisticcomputing power.

Although the present invention has been described above using theembodiment, the technical scope of the present invention is not limitedto the scope of the description of the above embodiment. It is apparentto those skilled in the art that various modifications and improvementscan be made in the above embodiment. From the description of the claims,it is apparent that aspects in which such modifications and improvementsare made can also be included in the technical scope of the presentinvention.

According to the above embodiment and modified example, a generationdevice, a generation method, a program, a recording medium described inthe following respective items can be realized.

(Article 1) A generation device for generating a hologram pattern fordisplaying a 3D object based on the 3D object to be displayed, thegeneration device including:

selecting means for selecting, as a cross section range in each crosssection of a plurality of cross sections into which the 3D object isdivided and which are parallel to the hologram pattern, the crosssection range being a range used for generating the hologram pattern, across section range overlapping cross section ranges in other crosssections in a case where the relevant cross section is perspectivelyseen from a previously determined observation point on the hologrampattern;

depth integrating means for calculating, for each of a plurality oflattice points in a coordinate system provided in one cross sectionrange, a depth integral function acquired by integrating an inversediffraction function for determining a hologram pattern for displayingpoints of the 3D object, with respect to respective lattice points inthe plurality of cross section ranges, the respective lattice pointsoverlapping the relevant lattice point in a case where the plurality ofcross section ranges are perspectively seen from the observation point;and

inverse Fourier transform means for generating the hologram pattern byperforming a two-dimensional inverse Fourier transform on the depthintegral functions with respect to the plurality of lattice points inthe one cross section range.

(Article 2) The generation device according to Article 1,

wherein the selecting means selects the plurality of cross sectionranges by performing a variable change from coordinate variablesrepresenting coordinates on each of the plurality of cross sections tovariables acquired by dividing the coordinate variables by a distance tothe relevant cross section,

the depth integrating means calculates the depth integral function byintegrating the inverse diffraction function in which the variablechange has been performed, with respect to a variable representing adistance from the hologram pattern to a cross section, and

the inverse Fourier transform means performs the two-dimensional inverseFourier transform with respect to the plurality of lattice points byperforming an inverse Fourier transform on the depth integral functionswith respect to the coordinate variables in which the variable changehas been performed.

(Article 3) The generation device according to Article 2,

wherein the inverse diffraction function is an integrand with respect tothe coordinate variables in an inverse function of the Fraunhoferdiffraction integral function, and

the selecting means selects the plurality of cross section ranges byperforming a variable change on the coordinate variables of theintegrand and setting an integration interval with respect to thecoordinate variables to a same previously determined interval for theplurality of cross section ranges in the inverse function of theFraunhofer diffraction integral function.

(Article 4) The generation device according to Article 2, wherein thedepth integrating means performs integration with respect to thevariable representing the distance from the hologram pattern to a crosssection by approximating a term representing a phase component of alight wave in the inverse diffraction function by a value independent ofthe coordinate variables.(Article 5) The generation device according to Article 2, wherein thedepth integrating means performs integration with respect to thevariable representing the distance from the hologram pattern to a crosssection by approximating a term representing a phase component of alight wave in the inverse diffraction function by a periodic functionhaving, as a period of the coordinate variables, a ratio of thecoordinate variables before the variable change to the coordinatevariables after the variable change.(Article 6) The generation device according to Article 1, furthercomprising display means for displaying the hologram pattern generatedby the inverse Fourier transform means.(Article 7) The generation device according to Article 1, wherein theselecting means selects, as each of the plurality of cross sectionranges, a range having one side which is proportional to a distance fromthe hologram pattern to the relevant cross section range and awavelength of a light wave and inversely proportional to an inter-pixeldistance of the hologram pattern.(Article 8) A generation device for generating a hologram pattern,including:

distance information acquiring means for acquiring, for each pixel of atwo-dimensional image acquired by projecting a 3D object to be displayedonto a predetermined plane, distance information representing a distancefrom the relevant pixel to a portion of the 3D object, the portion beingrecorded as the relevant pixel;

inverse diffraction function generating means for generating, for eachpixel of the two-dimensional image, an inverse diffraction function fordetermining a hologram pattern for displaying a portion of the 3D objectrecorded as the relevant pixel, based on the distance information at therelevant pixel; and

inverse Fourier transform means for generating the hologram pattern byperforming a two-dimensional inverse Fourier transform on the inversediffraction functions with respect to variables representing coordinatesin the two-dimensional image.

(Article 9) A method of generating a hologram pattern using a computer,the hologram pattern displaying a 3D object based on the 3D object to bedisplayed, the method including the steps of:

selecting, as a cross section range in each cross section of a pluralityof cross sections into which the 3D object is divided and which areparallel to the hologram pattern, the cross section range being a rangeused for generating the hologram pattern, a cross section rangeoverlapping cross section ranges in other cross sections in a case wherethe relevant cross section is perspectively seen from a previouslydetermined observation point on the hologram pattern, using thecomputer;

calculating, for each of a plurality of lattice points in a coordinatesystem provided in one cross section range, a depth integral functionusing the computer, the depth integral function being acquired byintegrating an inverse diffraction function for determining a hologrampattern for displaying points of the 3D object, with respect torespective lattice points in the plurality of cross section ranges, therespective lattice points overlapping the relevant lattice point in acase where the plurality of cross section ranges are perspectively seenfrom the observation point; and

generating the hologram pattern using the computer, by performing atwo-dimensional inverse Fourier transform on the depth integralfunctions with respect to the plurality of lattice points in the onecross section range.

(Article 10) A method of generating a hologram pattern using a computer,including the steps of:

acquiring, for each pixel of a two-dimensional image acquired byprojecting a 3D object to be displayed onto a predetermined plane,distance information using the computer, the distance informationrepresenting a distance from the relevant pixel to a portion of the 3Dobject, the portion being recorded as the relevant pixel;

generating, for each pixel of the two-dimensional image, an inversediffraction function for determining a hologram pattern for displaying aportion of the 3D object recorded as the relevant pixel, based on thedistance information at the relevant pixel using the computer; and

generating the hologram pattern using the computer, by performing atwo-dimensional inverse Fourier transform on the inverse diffractionfunctions with respect to variables representing coordinates in thetwo-dimensional image.

(Article 11) A program for generating, using a computer, a hologrampattern for displaying a 3D object based on the 3D object to bedisplayed, the program causing the computer to function as:

selecting means for selecting, as a cross section range in each crosssection of a plurality of cross sections into which the 3D object isdivided and which are parallel to the hologram pattern, the crosssection range being a range used for generating the hologram pattern, across section range overlapping cross section ranges in other crosssections in a case where the relevant cross section is perspectivelyseen from a previously determined observation point on the hologrampattern;

depth integrating means for calculating, for each of a plurality oflattice points in a coordinate system provided in one cross sectionrange, a depth integral function acquired by integrating an inversediffraction function for determining a hologram pattern for displayingpoints of the 3D object, with respect to respective lattice points inthe plurality of cross section ranges, the respective lattice pointsoverlapping the relevant lattice point in a case where the plurality ofcross section ranges are perspectively seen from the observation point;and

inverse Fourier transform means for generating the hologram pattern byperforming a two-dimensional inverse Fourier transform on the depthintegral functions with respect to the plurality of lattice points inthe one cross section range.

(Article 12) A program for generating a hologram pattern using acomputer, the program causing the computer to function as:

distance information acquiring means for acquiring, for each pixel of atwo-dimensional image acquired by projecting a 3D object to be displayedonto a predetermined plane, distance information representing a distancefrom the relevant pixel to a portion of the 3D object, the portion beingrecorded as the relevant pixel;

inverse diffraction function generating means for generating, for eachpixel of the two-dimensional image, an inverse diffraction function fordetermining a hologram pattern for displaying a portion of the 3D objectrecorded as the relevant pixel, based on the distance information at therelevant pixel; and

inverse Fourier transform means for generating the hologram pattern byperforming a two-dimensional inverse Fourier transform on the inversediffraction functions with respect to variables representing coordinatesin the two-dimensional image.

(Article 13) A recording medium on which the program according to anyone of Articles 11 and 12 is recorded.

According to the present invention, a hologram pattern can be generatedfast. Although particular embodiments of the present invention have beendescribed in detail, it should be understood that various changes,substitutions and alternations can be made therein without departingfrom spirit and scope of the inventions as defined by the appendedclaims.

The present invention can be realized in hardware, software, acombination of hardware and software. It may be implemented as a methodhaving steps to implement one or more functions of the invention, and/orit may be implemented as an apparatus having components and/or means toimplement one or more steps of a method of the invention described aboveand/or known to those skilled in the art. A visualization tool accordingto the present invention can be realized in a centralized fashion in onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system—or other apparatus adapted for carrying out the methodsand/or functions described herein—is suitable. A typical combination ofhardware and software could be a general purpose computer system with acomputer program that, when being loaded and executed, controls thecomputer system such that it carries out the methods described herein.The present invention can also be embedded in a computer programproduct, which comprises all the features enabling the implementation ofthe methods described herein, and which—when loaded in a computersystem—is able to carry out these methods.

Computer program means or computer program in the present contextinclude any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or afterconversion to another language, code or notation, and/or afterreproduction in a different material form.

Thus the invention includes an article of manufacture which comprises acomputer usable medium having computer readable program code meansembodied therein for causing one or more functions described above. Thecomputer readable program code means in the article of manufacturecomprises computer readable program code means for causing a computer toeffect the steps of a method of this invention. Similarly, the presentinvention may be implemented as a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the computer program product comprisingcomputer readable program code means for causing a computer to affectone or more functions of this invention. Furthermore, the presentinvention may be implemented as a program storage device readable bymachine, tangibly embodying a program of instructions executable by themachine to perform method steps for causing one or more functions ofthis invention.

It is noted that the foregoing has outlined some of the more pertinentobjects and embodiments of the present invention. This invention may beused for many applications. Thus, although the description is made forparticular arrangements and methods, the intent and concept of theinvention is suitable and applicable to other arrangements andapplications. It will be clear to those skilled in the art thatmodifications to the disclosed embodiments can be effected withoutdeparting from the spirit and scope of the invention. The describedembodiments ought to be construed to be merely illustrative of some ofthe more prominent features and applications of the invention. Otherbeneficial results can be realized by applying the disclosed inventionin a different manner or modifying the invention in ways known to thosefamiliar with the art.

1. A generation device for generating a hologram pattern, comprising:distance information acquiring means for acquiring, for each pixel of atwo-dimensional image acquired by projecting a 3D object to be displayedonto a predetermined plane, distance information representing a distancefrom the relevant pixel to a portion of the 3D object, the portion beingrecorded as the relevant pixel; inverse diffraction function generatingmeans for generating, for each pixel of the two-dimensional image, aninverse diffraction function for determining a hologram pattern fordisplaying a portion of the 3D object recorded as the relevant pixel,based on the distance information at the relevant pixel; and inverseFourier transform means for generating the hologram pattern byperforming a two-dimensional inverse Fourier transform on the inversediffraction functions with respect to variables representing coordinatesin the two-dimensional image.
 2. A method of generating a hologrampattern using a computer, comprising the steps of: acquiring, for eachpixel of a two-dimensional image acquired by projecting a 3D object tobe displayed onto a predetermined plane, distance information using thecomputer, the distance information representing a distance from therelevant pixel to a portion of the 3D object, the portion being recordedas the relevant pixel; generating, for each pixel of the two-dimensionalimage, an inverse diffraction function for determining a hologrampattern for displaying a portion of the 3D object recorded as therelevant pixel, based on the distance information at the relevant pixelusing the computer; and generating the hologram pattern using thecomputer, by performing a two-dimensional inverse Fourier transform onthe inverse diffraction functions with respect to variables representingcoordinates in the two-dimensional image.
 3. A computer program productcomprising a computer usable medium having computer readable programcode stored therein for causing generation of a hologram, the computerreadable program code means in said computer program product comprisingcomputer readable program code means for causing a computer to effectthe functions of a method comprising steps of: acquiring, for each pixelof a two-dimensional image acquired by projecting a 3D object to bedisplayed onto a predetermined plane, distance information using thecomputer, the distance information representing a distance from therelevant pixel to a portion of the 3D object, the portion being recordedas the relevant pixel; generating, for each pixel of the two-dimensionalimage, an inverse diffraction function for determining a hologrampattern for displaying a portion of the 3D object recorded as therelevant pixel, based on the distance information at the relevant pixelusing the computer; and generating the hologram pattern using thecomputer, by performing a two-dimensional inverse Fourier transform onthe inverse diffraction functions with respect to variables representingcoordinates in the two-dimensional image.